Multiple choice

There are two pipes in a cistern. One pipe can fill it with water in 32 hours, while the other pipe can empty it in 20 hours. How much time would it take to completely empty the cistern if both the pipes are opened together when 3/4th of the cistern is already full of water?

  1. 20 hours

  2. 24 hours

  3. 40 hours

  4. 36 hours

  5. 30 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rate of filling = 1/32. Rate of emptying = 1/20. Net rate = 1/32 - 1/20 = (5 - 8) / 160 = -3/160. The cistern is 3/4 full, so we need to remove 3/4 of the total volume. Time = (3/4) / (3/160) = (3/4) * (160/3) = 40 hours.

AI explanation

The net rate at which water is emptied when both pipes are open is the difference between their individual rates, calculated as 1/20 - 1/32. Finding a common denominator yields 8/160 - 5/160 = 3/160, meaning the two pipes together can empty 3/160 of the cistern in one hour. Since only 3/4 of the cistern is full, we divide this amount by the hourly emptying rate: (3/4) / (3/160) = 160/4, resulting in a total time of 40 hours to empty the filled portion.

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